 1.1 
Let \(G^*\)  be the regular representation of \(G\) . Since \(G^*\)  is contained in \(\operatorname{Aut}X\) , it is clear that \(\mathcal {B}\)  is also a block for the action of \(G^*\) . Hence, [1]} tells us that \(\mathcal {B}\)  is an orbit of some subgroup \(H^*\)  of \(G^*\) . If we let \(H\)  be the corresponding subgroup of \(G\) , then the \(H^*\)  orbit of an element \(b\)  of \(G\)  is precisely \(b + H\) , so it is a coset of \(H\) .
